Ahmet Brkovic scored at either end before further goals from Rowan Vine and Dean Morgan settled a frantic clash in Luton's favour.
Brkovic cancelled out his own first-half stoppage-time strike when he twisted and turned before beating the Hatters' inspired keeper Dean Kiely.
Carlos Edwards wriggled clear down the right and crossed for Vine to slide in past Luke Steele for Luton's second.
And Morgan sealed the win with a sweetly-struck curling free-kick.
606 DEBATE: Give your thoughts on the match
Luton boss Mike Newell on keeper Dean Kiely:
"We re-signed him on Friday for another month - though obviously now they can take him back at any time.
"Dean has told us he wants to get away from Portsmouth.
"It might be beyond us to take him permanently. A lot of things would have to happen if we were even to be in contention to take him."
Coventry boss Micky Adams:
"Their keeper got man of the match and rightly so, but that's about as well as we've played away from home this season in the first half.
"Goalkeeper Luke Steele is a doubt for Boxing Day trip to Ipswich with a gash on his knee.
"Andy Marshall is due to go in for an operation but we might have to cancel that for now."
Luton: Kiely, Foley, Barnett, Heikkinen, Emanuel, Edwards, Bell, Robinson (Coyne 63), Brkovic (Langley 83), Morgan (Feeney 81), Vine.
Subs Not Used: Beresford, Boyd.
Booked: Heikkinen, Vine, Morgan, Barnett.
Goals: Brkovic 45, Vine 66, Morgan 68.
Coventry: Steele, Clarke, Ward, Bischoff, Duffy, McKenzie, Doyle, Hughes, Cameron (Currie 74), Adebola (Virgo 74), John (Kyle 74).
Subs Not Used: Hall, Birchall
Goals: Brkovic 59 og.
Ref: A Taylor (Cheshire).